NUMERICAL SOLUTION WITH HIGHER ORDERnACCURACY FOR OPTION PRICING WITHnSTOCHASTIC VOLATILITY USING A GEOMETRICALnTRANSFORMATION
کد مقاله : 1055-FEMATH-FULL (R1)
نویسندگان:
1رحمان اکبری بنی *، 2محمد تقی جهاندیده، 3رضا مختاری
1دانشجو/دانشگاه صنعتی اصفهان
2هیات علمی / دانشگاه صنعتی اصفهان
3هیات علمی/دانشگاه صنعتی اصفهان
چکیده مقاله:
‎In this paper using a geometrical transformation we propose a‎n‎new compact finite difference (CFD) method based on the Alternating Direction Implicit (ADI) approach for solving‎nHeston equation that plays an important role in financial optionnpricing theory‎. ‎A feature of this time-dependent, two-dimensionalnconvection-diffusion-reaction equation is the presence of a mixednspatial-derivative term, which stems from the correlation between the two underlyingnstochastic processes for the asset price and its variance. ‎Thise method leads to a‎n‎system of linear equations involving banded matrices and‎n‎the rate of convergence of the method is of order $O(k^2+h_1^8+h_2^8)$ where $k$, $h_1$ and $h_2$ are time and space‎n‎step-sizes‎, ‎respectively‎. Stability analysis of the method is investigated bynthe matrix method. ‎Numerical results obtained by thenproposed method are compared with the exact solutions and the results obtained bynsome other methods which imply that our method is effective and applicable for solving such problems‎.‎
کلیدواژه ها:
Option pricing‎,nHeston equation‎, stochastic volatility, ‎compact finite difference scheme, geometrical transformation.
وضعیت : مقاله برای ارائه شفاهی پذیرفته شده است